Menominee Park is a super fun park.
They have shelters, ball parks, volleyball nets, a zoo, swimming, boat launching, places to sit and enjoy the lake, a little beach for swimming (if you don't mind letting your body touch Lake Winnebago water!)
The little Oshkosh playground is fun but I always feel nervous--there are lots of places that you can't see your child--so it's harder to watch little ones.
The park has another smaller playground on the other side that is much easier to keep an eye on the kids!
Of course it's THE place to be during Fourth of July week.